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October 27, 2014 14:19
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""" | |
====================================================================== | |
Repeated measures ANOVA on source data with spatio-temporal clustering | |
====================================================================== | |
This example illustrates how to make use of the clustering functions | |
for arbitrary, self-defined contrasts beyond standard t-tests. In this | |
case we will tests if the differences in evoked responses between | |
stimulation modality (visual VS auditory) depend on the stimulus | |
location (left vs right) for a group of subjects (simulated here | |
using one subject's data). For this purpose we will compute an | |
interaction effect using a repeated measures ANOVA. The multiple | |
comparisons problem is addressed with a cluster-level permutation test | |
across space and time. | |
""" | |
# Authors: Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr> | |
# Eric Larson <larson.eric.d@gmail.com> | |
# Denis Engemannn <denis.engemann@gmail.com> | |
# | |
# License: BSD (3-clause) | |
print(__doc__) | |
import os.path as op | |
import numpy as np | |
from numpy.random import randn | |
import mne | |
from mne import (io, spatial_tris_connectivity, compute_morph_matrix, | |
grade_to_tris) | |
from mne.stats import (spatio_temporal_cluster_1samp_test, | |
summarize_clusters_stc, f_threshold_twoway_rm) | |
from mne.minimum_norm import apply_inverse, read_inverse_operator | |
from mne.datasets import sample | |
############################################################################### | |
# Set parameters | |
data_path = sample.data_path() | |
raw_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif' | |
event_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif' | |
subjects_dir = data_path + '/subjects' | |
tmin = -0.2 | |
tmax = 0.3 # Use a lower tmax to reduce multiple comparisons | |
# Setup for reading the raw data | |
raw = io.Raw(raw_fname) | |
events = mne.read_events(event_fname) | |
############################################################################### | |
# Read epochs for all channels, removing a bad one | |
raw.info['bads'] += ['MEG 2443'] | |
picks = mne.pick_types(raw.info, meg=True, eog=True, exclude='bads') | |
# we'll load all four conditions that make up the 'two ways' of our ANOVA | |
event_id = dict(l_aud=1, r_aud=2, l_vis=3, r_vis=4) | |
reject = dict(grad=1000e-13, mag=4000e-15, eog=150e-6) | |
epochs = mne.Epochs(raw, events, event_id, tmin, tmax, picks=picks, | |
baseline=(None, 0), reject=reject, preload=True) | |
# Equalize trial counts to eliminate bias (which would otherwise be | |
# introduced by the abs() performed below) | |
epochs.equalize_event_counts(event_id, copy=False) | |
############################################################################### | |
# Transform to source space | |
fname_inv = data_path + '/MEG/sample/sample_audvis-meg-oct-6-meg-inv.fif' | |
snr = 3.0 | |
lambda2 = 1.0 / snr ** 2 | |
method = "dSPM" # use dSPM method (could also be MNE or sLORETA) | |
inverse_operator = read_inverse_operator(fname_inv) | |
# we'll only use one hemisphere to speed up this example | |
# instead of a second vertex array we'll pass an empty array | |
sample_vertices = [inverse_operator['src'][0]['vertno'], np.array([])] | |
# Let's average and compute inverse, then resample to speed things up | |
conditions = [] | |
for cond in ['l_aud', 'r_aud', 'l_vis', 'r_vis']: # order is important | |
evoked = epochs[cond].average() | |
evoked.resample(50) | |
condition = apply_inverse(evoked, inverse_operator, lambda2, method) | |
# Let's only deal with t > 0, cropping to reduce multiple comparisons | |
condition.crop(0, None) | |
conditions.append(condition) | |
tmin = conditions[0].tmin | |
tstep = conditions[0].tstep | |
############################################################################### | |
# Transform to common cortical space | |
# Normally you would read in estimates across several subjects and morph | |
# them to the same cortical space (e.g. fsaverage). For example purposes, | |
# we will simulate this by just having each "subject" have the same | |
# response (just noisy in source space) here. | |
# we'll only consider the left hemisphere in this example. | |
n_vertices_sample, n_times = conditions[0].lh_data.shape | |
n_subjects = 7 | |
print('Simulating data for %d subjects.' % n_subjects) | |
# Let's make sure our results replicate, so set the seed. | |
np.random.seed(0) | |
X = randn(n_vertices_sample, n_times, n_subjects, 4) * 10 | |
for ii, condition in enumerate(conditions): | |
X[:, :, :, ii] += condition.lh_data[:, :, np.newaxis] | |
# It's a good idea to spatially smooth the data, and for visualization | |
# purposes, let's morph these to fsaverage, which is a grade 5 source space | |
# with vertices 0:10242 for each hemisphere. Usually you'd have to morph | |
# each subject's data separately (and you might want to use morph_data | |
# instead), but here since all estimates are on 'sample' we can use one | |
# morph matrix for all the heavy lifting. | |
fsave_vertices = [np.arange(10242), np.array([])] # right hemisphere is empty | |
morph_mat = compute_morph_matrix('sample', 'fsaverage', sample_vertices, | |
fsave_vertices, 20, subjects_dir) | |
n_vertices_fsave = morph_mat.shape[0] | |
# We have to change the shape for the dot() to work properly | |
X = X.reshape(n_vertices_sample, n_times * n_subjects * 4) | |
print('Morphing data.') | |
X = morph_mat.dot(X) # morph_mat is a sparse matrix | |
X = X.reshape(n_vertices_fsave, n_times, n_subjects, 4) | |
# Now we need to prepare the group matrix for the ANOVA statistic. | |
# To make the clustering function work correctly with the | |
# ANOVA function X needs to be a list of multi-dimensional arrays | |
# (one per condition) of shape: samples (subjects) x time x space | |
X = np.transpose(X, [2, 1, 0, 3]) # First we permute dimensions | |
# finally we split the array into a list a list of conditions | |
# and discard the empty dimension resulting from the split using numpy squeeze | |
X = [np.squeeze(x) for x in np.split(X, 4, axis=-1)] | |
############################################################################### | |
# Prepare function for arbitrary contrast | |
# As our ANOVA function is a multi-purpose tool we need to apply a few | |
# modifications to integrate it with the clustering function. This | |
# includes reshaping data, setting default arguments and processing | |
# the return values. For this reason we'll write a tiny dummy function. | |
# We will tell the ANOVA how to interpret the data matrix in terms of | |
# factors. This is done via the factor levels argument which is a list | |
# of the number factor levels for each factor. | |
factor_levels = [2, 2] | |
# Finally we will pick the interaction effect by passing 'A:B'. | |
# (this notation is borrowed from the R formula language) | |
effects = 'A:B' # Without this also the main effects will be returned. | |
# Tell the ANOVA not to compute p-values which we don't need for clustering | |
return_pvals = False | |
# a few more convenient bindings | |
n_times = X[0].shape[1] | |
n_conditions = 4 | |
# A stat_fun must deal with a variable number of input arguments. | |
def stat_fun(*args): | |
# Inside the clustering function each condition will be passed as | |
# flattened array, necessitated by the clustering procedure. | |
# The ANOVA however expects an input array of dimensions: | |
# subjects X conditions X observations (optional). | |
# The following expression catches the list input | |
# and swaps the first and the second dimension, and finally calls ANOVA. | |
return mne.stats.ttest_1samp_no_p(*args) ** 2 | |
# get f-values only. | |
# Note. for further details on this ANOVA function consider the | |
# corresponding time frequency example. | |
############################################################################### | |
# Compute clustering statistic | |
# To use an algorithm optimized for spatio-temporal clustering, we | |
# just pass the spatial connectivity matrix (instead of spatio-temporal) | |
source_space = grade_to_tris(5) | |
# as we only have one hemisphere we need only need half the connectivity | |
lh_source_space = source_space[source_space[:, 0] < 10242] | |
print('Computing connectivity.') | |
connectivity = spatial_tris_connectivity(lh_source_space) | |
# Now let's actually do the clustering. Please relax, on a small | |
# notebook and one single thread only this will take a couple of minutes ... | |
pthresh = 0.0005 | |
f_thresh = f_threshold_twoway_rm(n_subjects, factor_levels, effects, pthresh) | |
# To speed things up a bit we will ... | |
n_permutations = 128 # ... run fewer permutations (reduces sensitivity) | |
X_ = (X[0] - X[2]) - (X[1] - X[3]) | |
print('Clustering.') | |
T_obs, clusters, cluster_p_values, H0 = clu = \ | |
spatio_temporal_cluster_1samp_test(X_, connectivity=connectivity, n_jobs=1, | |
threshold=f_thresh, stat_fun=stat_fun, | |
n_permutations=n_permutations, | |
buffer_size=None) | |
# Now select the clusters that are sig. at p < 0.05 (note that this value | |
# is multiple-comparisons corrected). | |
good_cluster_inds = np.where(cluster_p_values < 0.05)[0] | |
############################################################################### | |
# Visualize the clusters | |
print('Visualizing clusters.') | |
# Now let's build a convenient representation of each cluster, where each | |
# cluster becomes a "time point" in the SourceEstimate | |
stc_all_cluster_vis = summarize_clusters_stc(clu, tstep=tstep, | |
vertno=fsave_vertices, | |
subject='fsaverage') | |
# Let's actually plot the first "time point" in the SourceEstimate, which | |
# shows all the clusters, weighted by duration | |
subjects_dir = op.join(data_path, 'subjects') | |
# The brighter the color, the stronger the interaction between | |
# stimulus modality and stimulus location | |
brain = stc_all_cluster_vis.plot('fsaverage', 'inflated', 'lh', | |
subjects_dir=subjects_dir, | |
time_label='Duration significant (ms)') | |
brain.set_data_time_index(0) | |
brain.scale_data_colormap(fmin=5, fmid=10, fmax=30, transparent=True) | |
brain.show_view('lateral') | |
brain.save_image('cluster-lh.png') | |
brain.show_view('medial') | |
############################################################################### | |
# Finally, let's investigate interaction effect by reconstructing the time | |
# courses | |
import matplotlib.pyplot as plt | |
inds_t, inds_v = [(clusters[cluster_ind]) for ii, cluster_ind in | |
enumerate(good_cluster_inds)][0] # first cluster | |
times = np.arange(X[0].shape[1]) * tstep * 1e3 | |
plt.figure() | |
colors = ['y', 'b', 'g', 'purple'] | |
event_ids = ['l_aud', 'r_aud', 'l_vis', 'r_vis'] | |
for ii, (condition, color, eve_id) in enumerate(zip(X, colors, event_ids)): | |
# extract time course at cluster vertices | |
condition = condition[:, :, inds_v] | |
# normally we would normalize values across subjects but | |
# here we use data from the same subject so we're good to just | |
# create average time series across subjects and vertices. | |
mean_tc = condition.mean(axis=2).mean(axis=0) | |
std_tc = condition.std(axis=2).std(axis=0) | |
plt.plot(times, mean_tc.T, color=color, label=eve_id) | |
plt.fill_between(times, mean_tc + std_tc, mean_tc - std_tc, color='gray', | |
alpha=0.5, label='') | |
ymin, ymax = mean_tc.min() - 5, mean_tc.max() + 5 | |
plt.xlabel('Time (ms)') | |
plt.ylabel('Activation (F-values)') | |
plt.xlim(times[[0, -1]]) | |
plt.ylim(ymin, ymax) | |
plt.fill_betweenx((ymin, ymax), times[inds_t[0]], | |
times[inds_t[-1]], color='orange', alpha=0.3) | |
plt.legend() | |
plt.title('Interaction between stimulus-modality and location.') | |
plt.show() |
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